#include<vector>
#include<string>
using namespace std;
class Solution {
public:
    int minInsertions(string s) {
        int n = s.size();
        vector<vector<int>> dp(n, vector<int>(n, 0));

        for (int i = n - 1; i >= 0; i--) {
            for (int j = i; j < n; j++) {
                if (s[i] == s[j]) {
                    dp[i][j] = i + 1 < j ? dp[i + 1][j - 1] : 0;
                }
                else {
                    dp[i][j] = dp[i][j - 1] < dp[i + 1][j] ? dp[i][j - 1] + 1
                        : dp[i + 1][j] + 1;
                }
            }
        }
        return dp[0][n - 1];
    }
};